Effective density dependence of nuclear interaction in the relativistic hadron field theory

The fitting procedure of the NLRHF model was carried out with the outcome, that this model is not suitable for describing the more fundamental DBHF data. Various extensions have been used, however, without any improvement in the results. Subsequently, we proceeded to the fitting procedure of the DDRHF model. Here we presented one of the most important assets of this work - new functional forms of the effective density dependence. The 4-, 3-, and 2-parametric classes were introduced and their attributes discussed. They were used to extract the DDRHF model parametrizations from the DBHF data of Hofmann et al., Ma and Liu and van Dalen et al. with very good results. Although the proposed density functions correctly described the DBHF data of several groups, significant differences appeared when the high and low density extrapolations were considered. This undesirable feature is the reason why we carried out the partial fits, where only few DBHF data points were accounted for. This was done to see if any of proposed density dependencies is able to reproduce known, but not fitted data. All parametric classes failed the task, but one. The 2-parametric class exhibited a strong robustness and with minor exceptions reproduced all DBHF data in the whole density region. We believe that this class of density functions could provide more reliable extrapolations into high densities than other used parametrizations. Symmetric as well as asymmetric (pure neutron matter) nuclear matter properties were obtained for the fixed asymmetry ratios. Additionally, the standard nuclear matter along with the Λ matter in the β-equilibrium were examined from the perspective of the effective density dependence of the nuclear interaction. From the character of gained results we may conclude, that the choice of the density dependence significantly alters the high density properties of nuclear matter. Differences between parametrizations considering the extrapolations are distinct to such a measure that one could not rely on a specific density dependence only because it describes the underlying DBHF data. From the behaviour of the 2-parametric class in the fitting procedure we believe that this class is relatively well-founded and we would chose the results coming from this parametrizations as more credible, nevertheless, to support such a choice, connection to the experiment or observation has to be made. We briefly introduced a simple relativistic Hartree-Fock model in order to describe a novel procedure for extraction of the exchange Fock contributions. The RHF theory is an effective approach defined only on the Hartree level, without any explicit definition of exchange terms. Their effects could be effectively contained in the free parameters provided they are acquired from the fit to some sort of the Hartree-Fock theory. However, this would not lead to proper understanding of their role in the effective model. We have thus derived a theoretical procedure with which we are capable to map the Fock terms from the DHF theory onto mean-field one. New structure of the density dependent vertices that analytically account for the direct as well as exchange contributions was presented. This allows one to explicitly understand the density dependence coming from Fock contributions already on the mean-field level. (author)